Let $L$ be a lattice. In this paper, corresponding to a given congruence relation $\Theta$ of $L$, a congruence relation ${\Psi }_{\Theta }$ on $CS\left(L\right)$ is defined and it is proved that 1. $CS(L/\Theta )$ is isomorphic to $CS\left(L\right)/{\Psi }_{\Theta }$; 2. $L/\Theta$ and $CS\left(L\right)/{\Psi }_{\Theta }$ are in the same equational class; 3. if $\Theta$ is representable in $L$, then so is ${\Psi }_{\Theta }$ in $CS\left(L\right)$.